{
 "cells": [
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "# 线性回归\n",
    "可通过最小二乘法直接求解，但这并不是机器学习的思想，由此引入了梯度下降算法。"
   ],
   "id": "6f94c93042b62ec2"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## 主要内容：\n",
    "1. 线性回归方程实现\n",
    "2. 梯度下降效果\n",
    "3. 对比不同梯度下降策略\n",
    "4. 建模曲线分析\n",
    "5. 过拟合与欠拟合\n",
    "6. 正则化的作用\n",
    "7. 提前停止策略"
   ],
   "id": "957d7d8fb80c061d"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## sklearn api 文档：\n",
    "https://scikit-learn.org/stable/api/index.html"
   ],
   "id": "284ccf6739c33c8"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:21.510578Z",
     "start_time": "2025-03-14T10:12:20.936142Z"
    }
   },
   "cell_type": "code",
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "# 设置图片的相关字体大小\n",
    "plt.rcParams['axes.labelsize'] = 14\n",
    "plt.rcParams['xtick.labelsize'] = 12\n",
    "plt.rcParams['ytick.labelsize'] = 12\n",
    "np.random.seed(42)"
   ],
   "id": "f53a8ec29861f011",
   "outputs": [],
   "execution_count": 1
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## 回归方程\n",
    "当作巧合，机器学习中核心思想是迭代更新  \n",
    "\n",
    "![](Linear/1.png)"
   ],
   "id": "b901a4e38bb9a6e1"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:23.238567Z",
     "start_time": "2025-03-14T10:12:23.234839Z"
    }
   },
   "cell_type": "code",
   "source": [
    "X = 2 * np.random.rand(100, 1)      # rand生成均匀分布的随机数，取值范围为 [0, 1)\n",
    "y = 3 + 5 * X + np.random.randn(100, 1)     # randn生成标准正态分布（均值为 0，标准差为 1）的随机数"
   ],
   "id": "367898716daa932d",
   "outputs": [],
   "execution_count": 2
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:23.645365Z",
     "start_time": "2025-03-14T10:12:23.538872Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 折线图模块画散点图\n",
    "plt.plot(X, y, 'b.')\n",
    "plt.xlabel('X1')\n",
    "plt.ylabel('y')\n",
    "plt.axis((0, 2, 0, 15))"
   ],
   "id": "dd917372b8d88b75",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.0), np.float64(2.0), np.float64(0.0), np.float64(15.0))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 3
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:23.771554Z",
     "start_time": "2025-03-14T10:12:23.766489Z"
    }
   },
   "cell_type": "code",
   "source": [
    "X01 = np.c_[np.ones((100, 1)), X]       # c_合并数组\n",
    "theta_best = np.linalg.inv(X01.T.dot(X01)).dot(X01.T).dot(y)        # linalg.inv求逆矩阵\n",
    "# 矩阵的逆并不一定能够求出来\n",
    "theta_best"
   ],
   "id": "96a3fd4cfd653cb6",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.21509616],\n",
       "       [4.77011339]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 4
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:24.229280Z",
     "start_time": "2025-03-14T10:12:24.223929Z"
    }
   },
   "cell_type": "code",
   "source": [
    "X_new = np.array([[0], [2]])\n",
    "X_new = np.c_[np.ones((2, 1)), X_new]   # 列合并\n",
    "y_new = X_new.dot(theta_best)\n",
    "y_new"
   ],
   "id": "24c1cd9d5684c65a",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.21509616],\n",
       "       [12.75532293]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 5
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:24.319553Z",
     "start_time": "2025-03-14T10:12:24.230285Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.plot(X, y, 'b.')\n",
    "plt.plot(X_new[:, 1], y_new, 'r--')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')\n",
    "plt.axis((0, 2, 0, 15))"
   ],
   "id": "c2403fd44688ab0f",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.0), np.float64(2.0), np.float64(0.0), np.float64(15.0))"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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DI0fK5U2qVpXrwynMkmHpAPUxaCIiIlLA2iw0AHjuuVJ6fZYvl2UDJk2SBSlr1QLeeAM4cUL2NClM8GbpAPUxaCIiIlLg1llohZXY63PtGnDuHNCwIbBsmZwGOG0aYGfiMksHqI9BExGRzmhxDbGywlwCYdGi4o/l5QGm7ceBp58GEhIKHhg9WpYQSE6WM+QUFKS0hqUD1MeSA2DJASLSj9Jmb5FnmExySM48XNYCfyHGMA9DfD6GIS8PaNVKFqR0sLZSaef2ttIBjvL09zd7moiIdIKJwNph7vXp7PMb/ouH8BciMFR8JAOmnj2Bd99167kjIxkwqYF1moiIdKKkRGB+gXpe9KEpiM6X43TCYIDhscdkQcr27VVuGbkLe5qIiHSCicAqy88HcnIK7vfoIdeAGzkShkOHZO2BUgIm5qPpG4MmIiKdYCKwSm7cANaskZW7588v2H7//TIr/IMPgNtvL/VpWJiygF6DRyaCg4ngRKQvTAT2kGvXZEC0YAFw8qTc1qiRHCe1VrCpBLcmjgMy6E1JKXvvoSsnMzARnIiISsREYDe7fBmYO1cWpJw4UQZMtWoB8+YB+/fbHTABLExppvfJDEwEJyIiTXN0gVqHPf+8HPcEZOA0fTowYgRQsaLDT2nOR7u1p6ms5aPpfTIDe5qIiEizPJIHlJIib2aTJwMtWwJr18pv+XHjnAqYAOajmel9MgNzmsCcJiIiLXJ7HtChQ3LIbf16YOBAWbXbTAgWpnSTuDg5JJeXVxA86iWnicNzRESkSW4bytm1C4iNBf7734JtFy8CN2/KEgKAWwImQLa7rAZLZtHRQFSUPoNHBk1ERKRJLs8D2r4dmD0b2LJF3jcYgEceAWJigDvucLq9pJxeg0fmNBERkSZZywOaPNmJJ/z1VxkwlSsHDB8O/PUX8NlnxQImvdYQIvdj0ERERJoVHS1zmKZOlT1OCxcqTAi/cQP48EPgp58sQdCpvuNk1HXkCBAfDzRvXuwwFqCkkjARHEwEJyLyNHvKCNiVEJ6dXVCQ8sQJnGvQHrVP7ka+MJRaSJEFKPWHxS2JiMir2dubo6gwZEaGTO4ODQUmTABOnEBe9ZpYdLIffMRNAKUXUmQBSioNgyYiIvIYRypCl1rb5/33gfr1gRdeAM6elYHT0qX4ZW0K5onncRPlLceVFATpvYYQuR+DJiIi8hhHenNKLQxZowaQmQm0aCHzmJKTgaefRuOIinYFQSxASaVhThOY00RE5CnO5A2ZTEDaliSEb56PSh3DgWnT5AP5+cAPPwA9exbrKiqtkKK13CoWoNQPT39/M2gCgyYiIk9yqCL07t0FBSmFkL1LqamA0Vjq+WwFQXFxBUOFpSWJkzYxERxAVlYWZs2ahV69eiEoKAgGgwHx8fFW901KSkKvXr1QuXJlBAUF4YknnsC5c+c822AiIlLMXEYgMVH+tBmoCAH83/8B990HdOwIbNoktz38MLB5s6KACZCBUmRk0YDJkdwqIk1WBD9//jzmzJmD+vXro3Xr1ti6davV/UwmE7p27YrAwEDMnTsXWVlZWLhwIQ4ePIhdu3bBz8/Psw0nIiJFFFWEnj1b3gDZJTVkCDBjhsxdcpLblmghr6bJoKlOnTpIT09H7dq1sWfPHnTo0MHqfnPnzsXVq1exd+9e1K9fHwDQsWNH3HfffYiPj8fo0aM92WwiInLGjRtAVhZw223yfv/+wBtvAKNGyeqWoaEuO1XlynIVlcIJKpwpR6XR5PCc0WhE7dq1S93vs88+wwMPPGAJmADgP//5D5o2bYpPPvnEnU0kIiJXyc4Gli6V2diF10kJDwfS04ElS1waMMXFAXfeWTxg4kw5Ko0me5qUOHXqFM6ePYs7rCyy2LFjR3zzzTc2j83NzUVubq7lfmZmplvaSEREJcjIAJYtA956S9ZXAoAff5RBVMWK8n5goEtPeWsuEyCTwHfuBGwMahBZaLKnSYn09HQAcijvVnXq1MHFixeLBEaFxcbGIjAw0HILCQlxa1uJiKiQs2eBF1+UtQdiYuT9+vVlj9KRIwUBkxtYy2XKzweuXnXbKcmL6DZoys7OBiCH8m5VoUKFIvvcKiYmBhkZGZZbamqq+xpKRERFrVwJzJ0re5qaNwfWrJHB0vjxbg2YAFb9JufoNmiq+O8Hy1pvUk5OTpF9bmU0GhEQEFDkRkREbvL338C+fQX3x48HuneXJQT+/BMYNgwoX9728S5krvptDpx8fJjLRMrpNmgyD8uZh+kKS09PR1BQkNVeKCIi8pC9e4F+/WSJgPHjCzKvb7tN1l96+OHi3T5EGqbb39Z69eqhRo0a2LNnT7HHdu3ahTZt2ni+UURUJphMsjAjCyFaIQSwdatc0uSOO4DPPpPbatXSROIQi1qSM3QbNAHAY489hs2bNxfJSdqyZQuSk5PRv39/FVtGRN4qLk7mL/foIX/GxandouJUC+p+/hno3FkOvf34o0wWeuIJOQT33//K4kgqc2TBYCIzza49t2TJEly+fBlpaWlYtmwZHn30UbRt2xYAMHHiRAQGBiI1NRVt27ZF1apV8cwzzyArKwsLFixAcHAwdu/erXh4jmvPEZESziw26ylqrqd2YdknqPb0QAijEYboaLmgrgvrK7mCHt5DUs7j399Coxo0aCAAWL0dP37cst+ff/4pevbsKfz9/UXVqlXFkCFDxOnTp+06V0ZGhgAgMjIyXHwVRORN/u//hJBjTUVviYlqt0xKTRXCx6do23x95XaXy84W4r33hPjgAyGEEKtWCVHOcFPMQKyoY0gXq1a54ZwusmqVfF3Mr4+W20ol8/T3t2Z7mjyJPU1EpITWeykSE+WwobXtkZEuOklmJrB8ObBoEXDmDFC7Nkzbj6NBswp2vy4mkxwuCwvz/OtnMskhuSZNtPHekWM8/f2t65wmIiJPMk9X9/WV97W29IZbaxCdOwe89JKMGmfMkAFT/frACy/gyFGD3XlCaueGBQfLQFIr7x3pA3uawJ4mIrKPlnsp4uLkbLC8vIKgzumcpg8/BMaOlcubAMDttwPPPw8MHgyUL293D5xWeuzU7Oki12BPExGRxmm5lyI6WgYfiYnyp8MBU+GIplUrGTCZSwj89RcwfLilIKW9PXBamMGmdk8X6RN7msCeJiLSJ7f0lOzbB8TGAtWqydwls717gXbtAIOhxPYo6YFTu6dJ7fOT67CniYiISuXSnhJzQcqoKKB9eyAhAYiPBy5eLNinffsSAyZAeQ+c2rlhWujpIn1iTxPY00RE+uKynpL8fODrr+Xiub/9VvBEgwbJZO+ICFc2uxi1csPY0+Q92NNEREQlcllPyeLFQN++MmAyGoFx4+STr13r9oAJUC83TO2eLtIv9jSBPU1EpC8O95Tk5ABnz8pSAQBw/jzQsiUwbBgweTJQu7Y7m605Wp4FScp4+vu7nNvPQERELmXuKbm1tIDNL/4rV+QOb74JNG0q14gDgOrVgZMnLbPgyprgYAZLZB8GTUREOhQdLfO2S+wpOX8eePddYMkS4NIlua1cOVmoskYNeb+MBkxEjmDQRESkUzZ7Skwm2au0ciVw7Zrc1qyZTO4eMgTw8/NoO4m8BYMmIiJvs3Ur8Pbb8t/t2gExMcAjjxRkPhORQxg0ERE5SDPLcOzfD5w+DfTuLe8//jjw7beyavd995VaX4mIlGHJASIiB6i+DIcQwLZtQK9esjdp9Gjg+nX5WLlywLp1QM+eDJiIXIhBExGRnUwmGaOYp/zn58uZbCaTB04uBLB5M9ClC9CtG/D994CPD9C1K5CZ6YEGEJVdHJ4jIrJTScUl3TpMt20bMGECcPCgvG80AiNHAtOmAY0aufHERAQwaCIisltYmOzcubW4ZJMmbj5xxYoyYKpcWVbvnjwZqFPHzSclIjMOzxER2ckjy3BcuSLLBsyeXbCtQwdgzRpZkPKNNxgwEXkYl1EBl1EhIse4ZRmOCxdkQcrFi2VBSqNRro9SxpY4IVKCy6gQEemES5fhMJmARYtkl9W/BSlvNAxD+RdnAEFBLjoJETmDw3NERGr77DOZyP3WW8C1a9iHtuiPT+CfkoQ4RKtawdtkAhITPTQzkEjjGDQREakhJ6fg3126AL6+yO3UFb0N36E99iIB/XFT+HqulIEVqteiItIYBk1ERJ60fbus3P3ggwXbatUCkpLwa+zP+E5EASgoSGkuZeBpqtaiItIo5jQREbmbEMA33wCxscCOHXKbjw9w7FhBfaXQUISVU6mUgRWq1aIi0jD2NBERuUteHrBhA9C2LfDAAzJg8vOTXTbJycUKUnqilIHSHCVzLarC1ArgiLSCQRMRkbt88gkwaBDwxx+yIOXUqcDx48Dy5UDjxlYPiY6WFQYSE+XP6GjXNceeHCWP1KIi0hnWaQLrNBGRi2RlAUePAq1by/vXrwN33gk88ggwfryqpQNMJhko3Tr0l5JSciDkllpURC7COk1ERHpz8aIsRvnuu0BgoBx6K1dODsXt3QsYDKU/h5s5mqPk0lpURDrHoImIyFGnThUUpLx6VW6rVg04caJg+E0DAROg4np5RF6EOU1ERPY6cULOx2/USAZNV68CbdoAGzcCSUk285XUxBwlIuexp4mIyF6nTgHvvy//fc89wAsvAFFRmulVsiU6WjaTOUpEjmHQRERUmu3bZZ6SeSpb587A888DffrIat46whwlIscxaCIiskYI4LvvgLlzgV9+Afz9gYceAqpXl4/HxqrbPiLyOAZNRESF5eUBCQnAvHnAgQNym58fMGQIcPOmas0ymeQMuLAw9hQRqYWJ4ESkC0orWTvj7Je/4Vpoc+Dxx2XAVKkSMGWKLEi5ciVQu7b7Tl4CLpxLpA26DpoOHz6Mxx9/HMHBwfD398ftt9+OOXPm4Nq1a2o3jYhcyBNBQ1wc0P7hEJQzpeAibsO+vq/IWXILFwJ167r+hApx4Vwi7dBtRfDU1FS0atUKgYGBGDt2LIKCgrBz507Ex8ejb9+++OKLLxQ/FyuCE2mXo5WsS2UuSHnkCEyxay3nuA8/4Fd0Ro5vZefP4QKJiTJYtLY9MtLjzSHSFFYEV2jt2rW4fPkyfvnlF4SHhwMARo8ejfz8fHz44Ye4dOkSbrvtNpVbSUTOcrSStU1pabK20vLlloKUad2mIT+/FQDgR/T89yROnMOFWJSSSDt0OzyXmZkJAKhVq1aR7XXq1IGPjw/8/PzUaBYRuZg5aCjMoaDh6FE5rtWwIfDmmzJgat0a2LABde8Ld8053IBFKYm0Q7dBU+S//dLR0dE4cOAAUlNTsXHjRixbtgyTJk1CpUqV1G0gEbmES4KGn34CmjaVT3T9uqyt9M03wP79wMCBCG7gq+nAJDpaDkcmJsqf5nJRRORZus1pAoDXXnsNc+fORXZ2tmXbiy++iNdee63E43Jzc5Gbm2u5n5mZiZCQEOY0EWmYyWRnJeuLF4GgIPnvnBy5tEmbNkBMjM2ClCYTsHOnLNHUubN2giYiso45TXYIDQ1F165d8dhjj6FatWr4+uuvMXfuXNSuXRsTJkyweVxsbCxmz57twZYSkbMUVbIWAvjhB1mQMj1drgPn6wtUqAD8+SdQSp7j998XzFTz8ZEdU4726rCuEpH30W1P04YNGzBq1CgkJycjuNBfpJEjR+KTTz7ByZMnUa1aNavHsqeJtIZfsE7KywM+/1xW6d6/X24rXx7YsQPo0EHRU7hyll5cnOuCLyKyzdM9TbrNaXrvvffQtm3bIgETAPTt2xfXrl3DfvMfTiuMRiMCAgKK3IjUwsKFTrh+HfjgA6BFC2DAABkw+fsDkycDx44pDpiAkmfp2YN1lYi8l26DpjNnziAvL6/Y9hs3bgAAbqq43AGRUvyCddJvv8kunORkOfT28suyIOWiRXZ3D7lqlp6rgi8i0h7dBk1NmzbF/v37kZycXGT7xx9/DB8fH7Rq1UqllhEpV5a+YF2yDMrFi3ImnNk99wCPPiqrdp84AcyeXbCgrp1cNbXfZSUSiEhzdJvTtG3bNvTo0QPVqlXDhAkTUK1aNWzevBnffvstnnzySbz//vuKn4sVwUktbqt2rTFO5/ikpxcUpASAkydLTep2lN2z9KyIi5M9hnl5BcEXc5qIXM/T39+6DZoAYNeuXXjllVewf/9+XLhwAQ0bNsTw4cMxffp0lCunfGIggyZSk7d9wd6a1O5UYHj0KPDGG0B8vMxfAoBWrYB164CICDddgWu4IvgiopIxaFIBgyZSm7d8wVrrUWrUyIG101JSgBdeADZuLIi27r5b1li6/37AYHDTFRCRnrBOE5GXKqmsgKIaRBpnK6l9504H1k4zGIBPP5UH9eolA6h77nFr+4mISuNwInjv3r2xadMmqzPYiKioslBWwFZS+9WrpSRYmwtSzppVcGCDBsDixcC+fcC33zJgIiJNcHh4zsfHBwaDATVr1sSIESMQHR2NJjqdHsLhOXKnspLsXdp1FhuCzMsDNm2SBSn37ZMHHDyo+VwlItIO3RS3PHLkCKZPnw4fHx/Mnz8fzZo1w7333osNGzbgujlhk4jKTFmB0qbsBwfLHKbgmteB1auB8HCgf38ZMPn7A88+C9io4l+WuaRUAxG5hNOJ4Hl5edi8eTNWrVqF7777Dvn5+bjtttswbNgwPPnkk2jRooWr2uo27GkidyorPU1mJSa1/+9/QJ8+BRFA1arAxInApEkO11fyZlyOhahkup49l56ejg8++ACrV6/G8ePHAQB33XUXnnrqKQwcOBAVKlRw1alcikETuZu3lRWwixAFs92uXQNCQ4Fy5YDnnpMvSpUqqjVNy2v+lbVgm8gRug6aALl8yaZNmzB58mSkpaXJkxgMuO222zBjxgxMmTIFPreWy1UZgybyBG8pK6BYejrw1lvAtm3Ar78WlMnevx9o3hxQ+T9RWu/FSUx0oFQDURmj26ApOTkZq1atwocffohz587BaDSif//+GD58OPbt24clS5YgNTUVzz33HBYsWOCKU7oMgyYiFzp2DFiwQOYt5ebKbd9+K0sHaIQeenH00EYitekmERwAcnJysHbtWnTr1g3NmzfHwoULERQUhDfffBOnTp3CmjVr0KNHD0ydOhX//PMP7r77bnz44YeuajsRacmffwJDhwJNm8rlTnJzgc6dga++AqKi1G5dEXpIznfVWnhE5DoOF7ecMGEC1q9fj4yMDJQvXx4DBw7EmDFj0K1bN6v7G41GREVFYceOHQ43log0av9+oF27gvtRUQUFKTVYvdu8qK5dBTdVEB0tX8oyNaxLpGEOB03vvfceGjdujJiYGIwcORLVFcx8iYyMxMsvv+zoKYlIK4QAjh+Xa6QAQJs2QMeOcjzp+eeLBlAepiS529yLc2tyvhaDEm+oFk/kLRzOadqyZQvuvfdeV7dHFcxpIlIoP7+gIOWRI8DJk4D5M5ObCxiNqjbP3uTuMpecT+RldJsIrmcMmjxHy1O81aT51+X6dWDdOmD+fOCff+S2ihWBL78E/vMfddv2LyZOE5U9ukoEJ7JHWVh/zRGafl2uXQPefVd2xYwaJQOmqlWBmTOBEyc0EzAB+kjudgQrghNpB3uawJ4mT2AvgHWaf12OHpWz4fLzgVq1gClTZCKQBj8nmn8tHaD1WlJEamNPE3klb+0FcJbmXpfTp4GPPiq437gxMHUqsGyZjD6mTVMcMHm6h8TbpuibTAUBEyB/jhnDHiciNTk8e47IHnqZ4u1prnpdnM6JOn5cFqT84AOZv9ShA9CsmXxs/ny7n06tHhJvmqJfUkCt5+si0jP2NJFHeFsvgKu44nVRkhNls9fnr7+AJ56Q0dayZXIGXKdOQFaWw9ekdg9JcLBcZkTvv1vmgLow/keDSF0MmshjoqPlCE9iovzJ3AzJmddFSYBiNagymYCHHwYiIuRwXF4e0LOnbMSvvwLt2zt8PZobclRAi8nW/I8GkfYwERxMBCf9Km1RV1vJ0Sf+ykK9zg2AS5eARx8FYmKcCpQK00JCtj3DlVpPtmYtKSLbmAhORIqVNoRz+DAg8vPxCD7HGgwDIJCXBxxOryzzlw4dAhISXBYwAer3kNhTwkHtoUQlvGW4kcgbMGgi0rESA5QbN9D6wBr8hXB8jscwDGtxP74pCKoeegi4/Xa3tEutoVh7gyA9DiUSkXo4e45I54rNGAu6Biz5AFiwAEEnTyIIwGUEYgkmYK9PR4/1+qixZpq9M844q5OI7MGgicgLWAKU48eB0E7AuXPygVq1gOeew9UHx6LLmQCM8PK8GHuDID0t3EtE6mPQRKR3168Dfn7y36GhQJ06QKVKwPTpwIgRQMWKqAegXnMV2+ghjgRB3lTbiYjci7PnwNlzpFMpKcDChcAXXwBJSUDlynL7iRNAvXpAubL7fyLOOCMqGzz9/V12/6oS6dWhQ8C8ecD69bI7BQA2bZJFKgE5ZayMUyOfioi8H2fPeQEtFuYjN9i1C3jkESA8HFi7VgZM//kPsGULMHRokV35O0FE5HoMmnTOnpo0pGMnTwJ33gn897/y/qOPyiDqxx/lm28wWHbl7wQRkXswpwn6zWnSQuVlb+D0YrfukJ8P7N0rF841GzxYJnzPmAE0t57Vzd8JIipLWBGcFGNhPudprlfmxg3gww/lmnB33gkcO1bw2Lp1QHy8zYAJ4O8EEZE7MWjSMa6C7hxNLaGRnQ0sXSrf1OHD5Wy4KlWAgwcL9ik0BGcLfyeIiNyHQZOOqb3Gl95polcmKwuIjZX1lSZMkOUCataU206ckEud2IG/E0RE7sOcJug3p8mMNWkco4n8n8xMoH59ICNDBk7TpgEjRwIVKzr1tPydIKKygHWayG6sSeMYVZbQOHEC+PhjmcxtMAABAbJXqXJl4PHHgfLlXXIaPf5OaDIhn4ioEPY0Qf89TeQcd/bKmAOB5khC7TXzZTL3zZvADz8A993n2pM5SAvBSlxcQX6Zj48MZqOj1WkLEekHZ8/Zad++fejbty+CgoLg7++PiIgIvPvuu2o3i3QkOBiIjHR9wBAXBzxWfzcu9XgUNXuEA2vWyIDp3nuBqlVdezIHaWH2oKYS8omISqDr4bkffvgBDz74INq2bYuXXnoJlStXxtGjR2HiX1tyE6W9Mmn/O48GTw7C7/jJsm0THkHnr2JQ64EOtg/0IFvBSlSUZ3ucSkrI5zAdEWmJboOmzMxMDBs2DH369EFCQgJ8bp1nTeRi9gwh/XMuCHVxCjfhi3UYgvmYgSS0QGJloJZnm22TVoIVc5mEWxPyWSaBiLRGt5HG+vXrcebMGbz++uvw8fHB1atXkX/rNwCRi5Q4hHTjhlwLrnt34No1AEBYMx88afgATXAEI7AGSWihuUBAKzWdWCaBiPRCt0HTTz/9hICAAJw6dQrNmjVD5cqVERAQgHHjxiEnJ6fEY3Nzc5GZmVnkRlQSa70y5fOycW3he7jZuCkwbBiwdSuwejUA+YUf/f6dMPmGAtBmIKClYCU6WpZ6SEyUP5kETkRapNvZc61bt8aRf6sQRkdHIzIyElu3bsXixYvx+OOP4+OPP7Z57CuvvILZs2cX287Zc2RL4ZpOVZCJcViGyXgLtXEGAHAWNfC2YTJuf+dpDJsYWOQ4rddL0kMbiYis8fTsOd0GTY0bN8axY8cwduxYLFu2zLJ97NixWLFiBZKTkxEWFmb12NzcXOTm5lruZ2ZmIiQkhEETlSguDnh+9EX8k98EQbgEAEhBAyzANHyAUchBRS6OS0TkQSw5oFDFfysmDxo0qMj2wYMHAwB27txp81ij0YiAgIAiN3I/k0kOv+hucuPlywDkkNH+E0HI73wPboQ1x6Hn1yAMh/EexiMH8veRi+MSEXkv3QZNdevWBQDUqlV0LlLNmjUBAJcuXfJ4m8g2LdQDsltSEjBiBFC3LnDyJADZg1T9q9Uo//efCBg/DPk+RSt4ay3Zm4iIXEe3QVP79u0BAKdOnSqyPS0tDQBQo0YNj7eJrNNd8cI9e4DHHgPC/y1ImZ0N/Pe/BY8HBQE+PppKpCYiIvfTbdA0YMAAAEDcLV0Wq1atQrly5RAZGalCq8iakuoBaYYQcuywZ0+gQwfg88/ltoceAn77DZg0yephnPVFRFR26La4Zdu2bTFq1Ch88MEHuHnzJrp164atW7fi008/RUxMjGX4jtTniuKFbl8fLTMT6NsXyMqSjRs8WC6qGx5e6qF6XByXiIjsp9ugCQCWL1+O+vXrY/Xq1di0aRMaNGiAt956C88++6zaTaNCzMNYY8bIHiZ7h7HcspjrzZvA998D998PGAxAYCAweTJw4QIwbRoQGurkCYiIyNvotuSAK3l6ymJZ5Ug9oML1kcycmtafkwPExwNvvAEcPy4LUnbr5sATERGR2jz9/a3rnibSF0eGsVy2PtqVK8Dy5cCiRcDp03JbjRrAmTP2NYiIiMosBk2kaU7nQ2VnA3PnAkuWWOotoX59OQQ3ahTg7+/qJhMRkZfS7ew58i62Cl86Pa3fzw/YuFEGTLffLofmjhwBJkxgwERERHZh0ESqK63wpV3T+v/5B3jmGZm7BMgo6803gc8+A/76Cxg+HChfvoQnKKDbCuZEROQWTAQHE8HV5LJE7717gdjYgvpKK1bIKXcOcsWMPbeXSfDweYiItIZrz1GZ4lThSyHk7LeoKOCOO2RvkhCy3tK/FeMd4YoK5p5aNkaXy9MQEekUgyZSlTnRuzBFid7Z2UCXLkD37sAPP8iDhg4FDh4EvvjCqaDJ2Qrmnlo2RnfL0xAR6RyDJlKVXYnehUeSK1aUBSmNRmDcOBnprF0LREQ43SaHA7l/eWrZGF0sT0NE5EUYNJHqSk30zsmRkVR4OPDvgswAgHfekQe89x7QsKHL2uPsjD1ngy6lPHUeIiKSGDSRJgQHA5GRtwQmV64ACxbIgGjsWCApSdZbMgsLA2rXdkt7nFmI11bQBbh2Np7T5RiIiMgunD0Hzp7TnPPngXffBRYvLihIGRwsC1JGRwOVKqnaPKUKLxvz/ffKZ+PZOxvOkeVpiIi8gae/vxk0wfMvOqeIlyA3FwgJAc6dk/ebNQNmzACGDJGFKnXInrIKblmcmIjIS7HkgJdTe4q4Jgs2njxZ8G+jERg8GGjXDvj0U1mQcuRI3QZMgPKEbc6GIyLSNgZNHqT2l6LaAVsx+/YB/fsDoaHAr78WbJ83D9izB+jXryBhR8eUJmxzNhwRkbYxaPIgNb8U1Q7YLIQAtm0DevWStZQSEuS2xMSCfSpUAAwGDzfMfZQmbHM2HBGRtjFo8iBPfineOgzn6oCtpGE+q48JgfPxm5HRsgvQrZvMjPbxkblK//sf8OKLjjVEJ5TMxuNsOCIibWPQ5EGe+lK0NgznyoCtpGE+W4998H4eMkdOQuBfvyIHRiR1GysjuY8+Alq2dPxidcRqWYVbOFPqgIiI3Iuz56DO7Dl3TREvaabW99/LIbm8vIKAzZFFaG09P1DwmB9yMQgfY6PPYGz7zQ933gk8kR+P5kjC23gW53zr2L8oLxERUSGe/v4u5/YzUDHBwe4LFkoahouOlmvbOhOwlfT8QgD++VcwBivwHBahLtJhyBf45ZeRyM8H1mBEoYPkMQyaiIhILxg0eRnzMNytPUHmYThnAzZbz9+02gVU/uBdnMBiBOESACAVwbhp8EOXLiW3iYiISA+Y0+Rl3J03devz+/ncxIEez6HunfUR8PYcBOES/kFTjEIcmvocReT7Q9ChAxOciYhI/5jTBO9cRsXZvKnSqpYXef4R/wG2bAHatgViYmDq+CiOHPctdm4lbWK1dCIiUorLqKjAG4MmZ5S4lMf+/cDChcCiRUCtWnLb7t3AxYtAz55O1VfiEiJERGQPBk0qYNBUwNbsuLSN21Fz1Vzgu+/kxuefB2Jj3X5ezrAjIiJbuPYcqaro7DiB3vgGW/O6oGa/rjJg8vEBBg2SN7edV+ISIkREpCWcPeci3pKLY54dJ/LzsQN34y78BgAQfn4wjBgBTJ8ONG7stvNyhh0REWkVe5pcQHML4Trqxg3L7DgfXx/sQztkoRIO9pwCw/HjcsqbGwImQN9LiJS0pAwREXkP5jTBuTFRr8jFycqSEcqiRcAXXwB33AGTCTix+yxCm5RDvZZBHmuKO6uluwOT14mI1MNEcBU486InJsoeJmvbIyNd0z63uXABWLxY3i5elNuio4FVq9Rtl054RcBMRKRjXEZFZ3SZi3PqlOxVWrECuHpVbgsLA2bMAIYOVfQU3pLD5YySktfL6mtCROTNmNPkJGdzcTyeDyOE7AJbtEgGTG3aABs3AklJspfJaCz1Kbwmh8tJ5oC5MM0HzERE5DAGTS4QHS2HZBIT5U+lOS0eCz4OHgRu3pT/NhiACROArl2Bb78F9u0DBgwoiPpKYTIV5PAA8ueYMWUzCVrPyetERGQ/5jRBneKWHsmH2bFDFqD8+mvgo4+AIUPkdnPWsgN0ncPlJnpLXici8hbMaSoj3JYPI4QsQhkbC2zfLrf5+ACHDll2MaX5OJyPpMscLjcLDmawRERUFnB4zg6uzD9yeT6MEMAnnwDt2gH33y8DJj8/4KmngH/+AV5/HYDzQ4IckiIiorLKq4Km119/HQaDARERES5/blfnH7k8+DAYgKVLgQMHgEqVgOeeA44dkyf5NxJzVT6SozlcREREeuY1OU0mkwnNmjWDwWBAaGgo/vzzT8XHljYm6s78I4fzYbKygPffB554AqheXW77v/+TPUwTJgDVqhU7hPlIRETkTZjT5KCpU6fizjvvRF5eHs6fP+/S53ZnPR5b+TA26yBdvCiLUb77rvz35cvA7NnysR49rEdF/2I+EhERkeO8Ynhu27ZtSEhIwNtvv+2W5/d0PZ4FC4D69W8ZCkxLA6ZOlQ+88ooMmJo0AZo2Vfy8zEciIiJynO57mvLy8jBx4kQ8+eSTaNmypaJjcnNzkZuba7mfmZlZ4v7mYGPMGNnD5Opgo3Cv0oYNwPTpBY/l5wtkPzUJovxKGK5flxtbtwZiYoB+/RTXVzKLjgaiojhFnoiIyF66D5qWL1+OEydO4KefflJ8TGxsLGabh7QUcjTYKG25kcILvhoM1p7BAKPIkQFTly4yWOrd29bOinCKPBERkf10PTx34cIFvPzyy3jppZdQo0YNxcfFxMQgIyPDcktNTVV0XHCwTJhWGnCUNuPu1tlsQgB3iR34Cg+gNQ5Y9os1vIizCdtkkvf99zsVMBEREZFjdN3TNHPmTAQFBWHixIl2HWc0GmFUsMaaM2xN74+KKgi6ChLMBaLwPWIQi27YBgC4gioYjI8BAOPmh6LmY6FubS8RERGVTLdB0+HDh7Fy5Uq8/fbbSEtLs2zPycnBjRs3kJKSgoCAAAQFBanUvtJn3IU1ysMAw+eYIWLRDvsBANdRHh8ahmO+mA4fH2D+fJn/TUREROrSbZ2mrVu3onv37iXu88wzzyiaUeeOOg+Kajt17w5s3QoAuAp/vG8Yg1rzn8M9g4KZqE1ERFQK1mlSKCIiAps2bSq2febMmbhy5QreeecdNG7cWIWWSdZm3MW9exXBdSoA+HfG2/33A3/8gcwRk/C/bhPRr301S5BUFoOl0pLmiYiI1KTbniZbIiMjcf78eZdWBHeGyQSk7L+Elj8vQWD8O8B77wEDBsgHr12TEVWVKi49px4VnkXo4yMDTi7PQkREJfF0T5OuZ89pXno6gt+Zhi6D6yPwzZeBCxdkISYzf38GTHDdmnhERETupNvhOVu2/psj5IhTp4C9e10wPHT0qCzrvXo1YC5I2apVQUFKKsKdy9QQERG5itcFTc4ID5e1kkobHio192bECOCXX+S/774beOEFpwtSejOuiUdERHrA4blCzNldJQ0PWS1Y+euvwKVLBTtNny6DpG3bZPDEgpQl4pp4RESkB16XCO4IcyIZkAGgIJEsMVFWADcrWkZAoCd+wAuIRTf8DLz6KjBzpmcbbgc9zEwzmbgmHhERKcdEcI2wNjx0+DCA/Dw8hgTswR34Hr3QDT8jv1x5oJRFf9VU2nIuWmHvMjVERESexKCpEJ9/Xw1bw0Ot/7cWh9ACCeiP9tiHq/DHO4ZncebXY8Abb3i+wQpwZhoREZFrMBG8kD//BM6csT08FLR/C4KQjEuoisWYiKU+kzB3ZXXU6eD5tirFmWlERESuwaCpkHr1gObN/71z6RKwZAnw6KNyWh0APP88EBGBaw+MQdfTVTBKB7k3nJlGRETkGgyabpWeDrz1FrBsGZCVBSQnA2vXysduvx24/XbUA1DvdlVbqZi15Vw4M42IiMh+DJoKmzwZWLcOyM2V91u2BB54QN02uUB0NBAVxZlpREREzmDJARSasoh/Cw507iyrd/fpw/pKREREGuXpkgPsaSrs3nuBl18G7rmHwRIREREVwaCpsM8/BzwQqRIREZH+sE4TERERkQIMmoiIiIgUYNBEREREpACDJiIiIiIFGDQRERERKcCgSWdMJiAxkQvuEhEReRqDJh2JiwMaNAB69JA/4+Lcdy4GZ0REREUxaNIJkwkYPbpg4d38fLmenDuCGk8GZ0RERHrBoEknDh8uCJjM8vLkenKu5MngjIiISE8YNOlEWBjgc8u75esrF+B1JU8FZ0RERHrDoEkngoOBlStloATInytWyO2u5KngjIiISG8YNOlIdDSQkiITtFNS5H1X81RwRkREpDcGIYRQuxFqy8zMRGBgIDIyMhDgwgV7TSY53BUWpr+gw2SSQ3JNmuiv7UREVDa46/vbFvY0uYneZ6AFBwORkQyYiIiIzBg0uQFnoBEREXkfBk1uwBloRERE3odBkxtwBhoREZH3YdDkBpyBRkRE5H3Kqd0AbxUdDURFcQYaERGRt2DQ5EbBwQyWiIiIvAWH54iIiIgUYNBEREREpACDJiIiIiIFdBs07d69GxMmTEB4eDgqVaqE+vXrY8CAAUhOTla7aUREROSFdJsIPn/+fOzYsQP9+/dHq1atcPr0aSxZsgTt2rXDb7/9hoiICLWbSERERF5Etwv2/vrrr7jjjjvg5+dn2Xb48GG0bNkS/fr1w0cffaT4uTy94B8RERE5z9Pf37rtaercuXOxbWFhYQgPD0dSUpIKLSIiIiJvptugyRohBM6cOYPw8PAS98vNzUVubq7lfmZmprubRkRERDqn20Rwa9atW4dTp05h4MCBJe4XGxuLwMBAyy0kJMRDLSQiIiK90m1O063+/vtvdOrUCeHh4di+fTt8zQu/WWGtpykkJIQ5TURERDrCnCYHnD59Gn369EFgYCASEhJKDJgAwGg0wmg0eqh1RERE5A10HzRlZGSgd+/euHz5MrZv3466deuq3SQiIiLyQroOmnJycvDggw8iOTkZP/30E1q0aKF2k4iIiMhL6TZoysvLw8CBA7Fz50588cUXuOuuu9RuEhEREXkx3QZNU6ZMwZdffokHH3wQFy9eLFbMcujQoSq1jIiIiLyRbmfPRUZG4ueff7b5uD2XxYrgRERE+sPZcwpt3bpV7SYQERFRGeJVxS2JiIiI3IVBExEREZECDJqIiIiIFGDQRERERKQAgyYiIiIiBRg0ERERESnAoImIiIhIAQZNRERERAowaCIiIiJSgEETERERkQIMmoiIiIgUYNBEREREpACDJiIiIiIFGDQRERERKcCgiYiIiEgBBk1ERERECjBoIiIiIlKAQRMRERGRAgyaiIiIiBRg0ERERESkAIMmIiIiIgUYNBEREREpwKCJiIiISAEGTUREREQKMGgiIiIiUoBBExEREZECDJqIiIiIFGDQRERERKQAgyYiIiIiBRg0ERERESnAoImIiIhIAQZNRERERAowaCIiIiJSgEETERERkQIMmoiIiIgUYNBEREREpICug6bc3FzMmDEDdevWRcWKFdGpUyf8+OOPajeLiIiIvJCug6YRI0Zg0aJFGDJkCN555x34+vri/vvvxy+//KJ204iIiMjLGIQQQu1GOGLXrl3o1KkTFixYgKlTpwIAcnJyEBERgZo1a+LXX39V/FyZmZkIDAxERkYGAgIC3NVkIiIiciFPf3/rtqcpISEBvr6+GD16tGVbhQoVEB0djZ07dyI1NVXF1hEREZG3Kad2Axy1f/9+NG3atFhk2bFjRwDAgQMHEBISYvXY3Nxc5ObmWu5nZGQAkBErERER6YP5e9tTg2a6DZrS09NRp06dYtvN29LS0mweGxsbi9mzZxfbbivIIiIiIu26cOECAgMD3X4e3QZN2dnZMBqNxbZXqFDB8rgtMTExeO655yz3L1++jAYNGuDkyZMeedG1IjMzEyEhIUhNTS1TuVy8bl53WcDr5nWXBRkZGahfvz6CgoI8cj7dBk0VK1YsMsRmlpOTY3ncFqPRaDXgCgwMLFO/bGYBAQG87jKE11228LrLlrJ63T4+nknR1m0ieJ06dZCenl5su3lb3bp1Pd0kIiIi8mK6DZratGmD5OTkYsnbv//+u+VxIiIiIlfRbdDUr18/5OXlYeXKlZZtubm5WL16NTp16mRXUrfRaMSsWbOsDtl5M143r7ss4HXzussCXrdnrlu3xS0BYMCAAdi0aRMmT56MJk2aYM2aNdi1axe2bNmCrl27qt08IiIi8iK6DppycnLw0ksv4aOPPsKlS5fQqlUrvPrqq4iKilK7aURERORldB00EREREXmKbnOaiIiIiDyJQRMRERGRAl4RNOXm5mLGjBmoW7cuKlasiE6dOuHHH39UdOypU6cwYMAAVK1aFQEBAXjooYdw7Ngxq/vGxcWhefPmqFChAsLCwrB48WJXXobdHL3uzz//HAMHDkSjRo3g7++PZs2aYcqUKbh8+XKxfUNDQ2EwGIrdxo4d64YrUsbR637llVesXou5ivytvOX9tvUeGgwGhIWFFdnX1n7z5s1z12WVKisrC7NmzUKvXr0QFBQEg8GA+Ph4xcdfvnwZo0ePRo0aNVCpUiV0794d+/bts7rvl19+iXbt2qFChQqoX78+Zs2ahZs3b7roSuzjzHVv2bIFo0aNQtOmTeHv749GjRrhySeftFrbLjIy0up73qtXLxdfkTLOXHd8fLzN3+HTp08X299b3m9b76HBYED58uWL7Kulv+m7d+/GhAkTEB4ejkqVKqF+/foYMGAAkpOTFR2vxmdbtxXBCxsxYgQSEhLw7LPPIiwsDPHx8bj//vuRmJiILl262DwuKysL3bt3R0ZGBl544QWUL18eb731Frp164YDBw6gWrVqln1XrFiBsWPH4rHHHsNzzz2H7du3Y9KkSbh27RpmzJjhicssxtHrHj16NOrWrYuhQ4eifv36OHjwIJYsWYJvvvkG+/btK1ZNvU2bNpgyZUqRbU2bNnXLNSnh6HWbLVu2DJUrV7bc9/X1LbaPN73fb7/9NrKysopsO3HiBGbOnImePXsW2/++++7DsGHDimxr27atay7CAefPn8ecOXNQv359tG7dGlu3blV8bH5+Pvr06YM//vgD06ZNQ/Xq1fHee+8hMjISe/fuLRI0fvvtt3j44YcRGRmJxYsX4+DBg3jttddw9uxZLFu2zA1XVjJnrnvGjBm4ePEi+vfvj7CwMBw7dgxLlizB5s2bceDAAdSuXbvI/sHBwYiNjS2yTa0Cwc5ct9mcOXPQsGHDItuqVq1a5L43vd8vvvginnzyySLbrl69irFjx1r9jGvlb/r8+fOxY8cO9O/fH61atcLp06exZMkStGvXDr/99hsiIiJsHqvaZ1vo3O+//y4AiAULFli2ZWdni8aNG4u77rqrxGPnz58vAIhdu3ZZtiUlJQlfX18RExNj2Xbt2jVRrVo10adPnyLHDxkyRFSqVElcvHjRRVejnDPXnZiYWGzbmjVrBADx/vvvF9neoEGDYtetJmeue9asWQKAOHfuXIn7edv7bc2rr74qAIgdO3YU2Q5AjB8/3un2ulJOTo5IT08XQgixe/duAUCsXr1a0bEbN24UAMSnn35q2Xb27FlRtWpVMWjQoCL7tmjRQrRu3VrcuHHDsu3FF18UBoNBJCUlOX8hdnLmun/++WeRl5dXbBsA8eKLLxbZ3q1bNxEeHu6SNruCM9e9evVqAUDs3r271H296f22Zu3atQKAWLduXZHtWvqbvmPHDpGbm1tkW3JysjAajWLIkCElHqvWZ1v3w3MJCQnw9fXF6NGjLdsqVKiA6Oho7Ny5E6mpqSUe26FDB3To0MGy7fbbb8e9996LTz75xLItMTERFy5cwNNPP13k+PHjx+Pq1av4+uuvXXhFyjhz3ZGRkcW2PfLIIwCApKQkq8dcv34dV69eda7RLuDMdZsJIZCZmQlhY+Kot73f1qxfvx4NGzZE586drT6enZ1tWcdRbUajsVjPiFIJCQmoVasWHn30Ucu2GjVqYMCAAfjiiy8s61ceOnQIhw4dwujRo1GuXEEH/NNPPw0hBBISEpy7CAc4c91du3YtthZX165dERQUZPMzfvPmzWI9kmpw5roLu3LlCvLy8qw+5m3vtzXr169HpUqV8NBDD1l9XAt/0zt37gw/P78i28LCwhAeHm7z99RMrc+27oOm/fv3o2nTpsUWKOzYsSMA4MCBA1aPy8/Px//+9z/ccccdxR7r2LEjjh49iitXrljOAaDYvu3bt4ePj4/lcU9y9LptMY/3V69evdhj//d//wd/f39UrlwZoaGheOeddxxrtAu44robNWqEwMBAVKlSBUOHDsWZM2eKnQPw3vd7//79SEpKwuDBg60+Hh8fj0qVKqFixYpo0aIF1q9f73C71bZ//360a9euWADRsWNHXLt2zZI7Yes9r1u3LoKDg1V5z10tKysLWVlZVj/jycnJqFSpEqpUqYLatWvjpZdewo0bN1RopWt0794dAQEB8Pf3R9++fXH48OEij3v7+33u3Dn8+OOPePjhh1GpUqVij2vpb/qthBA4c+aM1d/TwtT6bOs+pyk9PR116tQptt28LS0tzepxFy9eRG5ubqnHNmvWDOnp6fD19UXNmjWL7Ofn54dq1arZPIc7OXrdtsyfPx++vr7o169fke2tWrVCly5d0KxZM1y4cAHx8fF49tlnkZaWhvnz5zt+AQ5y5rpvu+02TJgwAXfddReMRiO2b9+OpUuXYteuXdizZ48lIPH293vdunUAgCFDhhR7rHPnzhgwYAAaNmyItLQ0LF26FEOGDEFGRgbGjRvnYOvVk56ebnV1gMKvW8uWLS0J0rZeYzXec1d7++23cf36dQwcOLDI9saNG6N79+5o2bIlrl69ioSEBLz22mtITk7Gxo0bVWqtY/z9/TFixAhL0LR3714sWrQInTt3xr59+yzLa3n7+71x40bcvHnT6mdca3/Tb7Vu3TqcOnUKc+bMKXE/tT7bug+asrOzra45Y54RlZ2dbfM4AIqOzc7OLtaFWHhfW+dwJ0ev25r169cjLi4O06dPLzab6ssvvyxyf+TIkejduzcWLVqEiRMnIjg42IHWO86Z637mmWeK3H/sscfQsWNHDBkyBO+99x6ef/55y3N46/udn5+PDRs2oG3btmjevHmxx3fs2FHk/qhRo9C+fXu88MILGDFiRLFJAlqn9HUr7e/BrQuD6822bdswe/ZsDBgwAD169CjyWFxcXJH7TzzxBEaPHo33338fkydPxp133unJpjplwIABGDBggOX+ww8/jKioKHTt2hWvv/46li9fDsD73+/169ejRo0auO+++4o9prW/6YX9/fffGD9+PO666y4MHz68xH3V+mzrfniuYsWKlrHLwsz5GLb+yJu3Kzm2YsWKuH79utXnycnJUeWLxNHrvtX27dsRHR2NqKgovP7666XubzAYMHnyZNy8edOhWS3OctV1mw0ePBi1a9fGTz/9VOQc3vp+//zzzzh16pTV/4Fa4+fnhwkTJuDy5cvYu3ev8gZrhNLXrbS/B3oLFgv7+++/8cgjjyAiIgKrVq1SdIx5ZlXhz4VedenSBZ06dSr2GQe88/0+duwYdu7ciYEDBxbJ4bFF7b/pZqdPn0afPn0QGBhoyeEsiVqfbd0HTXXq1LFae8S8zda02aCgIBiNRkXH1qlTB3l5eTh79myR/a5fv44LFy6oMjXX0esu7I8//kDfvn0RERGBhIQERR8wAJYu7osXL9rRYtdwxXXfKiQkpMi1eOv7Dciubx8fHwwaNEjxudV8v52l9HUzd93b2let6ffOSk1NRc+ePREYGIhvvvkGVapUUXScnt9za6x9xgHve78BWHIQlf7HCFD//c7IyEDv3r1x+fJlfPfdd4pef7U+27oPmtq0aYPk5ORiXWy///675XFrfHx80LJlS+zZs6fYY7///jsaNWpk+QNjfo5b992zZw/y8/NtnsOdHL1us6NHj6JXr16oWbMmvvnmmyJ1i0pjLv5Zo0YN+xrtAs5e962EEEhJSSlyLd74fgPyf1qfffYZIiMj7fpDoeb77aw2bdpg3759yM/PL7L9999/h7+/v6U2ja33PC0tDSaTSZX33FkXLlxAz549kZubi++//95qTocten7PrTl27Jiiz7ie32+z9evXo3HjxnYNq6r5fufk5ODBBx9EcnIyNm/ejBYtWig6TrXPtl0FCjTot99+K1a/JicnRzRp0kR06tTJsu3EiRPF6jHMmzevWE2Pv//+W/j6+ooZM2ZYtl27dk0EBQWJBx54oMjxQ4cOFf7+/uLChQuuvqxSOXPd6enpolGjRqJu3bri+PHjNs9x4cIFcfPmzSLbrl+/Lu6++27h5+dnqSniSc5c99mzZ4s939KlSwUAsWjRIss2b3u/zT7//HMBQMTFxVl93Nrrk5mZKRo3biyqV69erJ6KGkqqX5OWliaSkpLE9evXLds2bNhQrJbLuXPnRNWqVcXAgQOLHH/77beL1q1bF/mdnzlzpjAYDOLQoUOuvxg72HvdWVlZomPHjqJKlSpiz549Np83IyND5OTkFNmWn58vBg4cKACIvXv3uuwaHGHvdVv7Hf76668FADFp0qQi273p/Tbbt2+fACBeeuklq8+rtb/pN2/eFH379hXlypUTX3/9tc39tPTZ1n3QJIQQ/fv3F+XKlRPTpk0TK1asEJ07dxblypUTP//8s2Wfbt26iVtjRPMXQs2aNcUbb7wh3nrrLRESEiLq1q1b7MNn/nLt16+feP/998WwYcMEAPH666975BqtcfS6W7duLQCI6dOni7Vr1xa5/fDDD5b9Vq9eLRo3bixmzJghli9fLubOnSsiIiIEADF37lyPXeetHL3uihUrihEjRog333xTLF26VAwaNEgYDAbRpk0bcfXq1SL7etP7bfbYY48Jo9EoLl++bPXxWbNmidatW4uZM2eKlStXitmzZ4sGDRoIg8EgPvroI7dck1KLFy8Wr776qhg3bpwAIB599FHx6quvildffdVyPcOHDxcAivxH4ObNm+LOO+8UlStXFrNnzxZLly4V4eHhokqVKuLvv/8uco6vvvpKGAwG0aNHD7Fy5UoxadIk4ePjI5566ilPXmoRjl73Qw89JACIUaNGFfuMb9q0ybJfYmKiqF27tpg8ebJYunSpWLhwobj77rsFADF69GgPX20BR6+7SZMmon///mL+/Pli+fLlYvTo0aJcuXIiJCREnD59usg5vOn9NpsyZYoAUOx320xrf9OfeeYZAUA8+OCDxX5P165da9lPS59trwiasrOzxdSpU0Xt2rWF0WgUHTp0EN99912RfWx9maSmpop+/fqJgIAAUblyZfHAAw+Iw4cPWz3PypUrRbNmzYSfn59o3LixeOutt0R+fr5brkkJR68bgM1bt27dLPvt2bNHPPjgg6JevXrCz89PVK5cWXTp0kV88sknnrg8mxy97ieffFK0aNFCVKlSRZQvX140adJEzJgxQ2RmZlo9j7e830LIHoUKFSqIRx991Obz//DDD+K+++4TtWvXFuXLlxdVq1YVPXv2FFu2bHH5tdirQYMGNn9nzX9IbX2ZXLx4UURHR4tq1aoJf39/0a1bN5sVozdt2iTatGkjjEajCA4OFjNnzrT6P3pPcfS6SzquQYMGlv2OHTsm+vfvL0JDQ0WFChWEv7+/aN++vVi+fLmqv+uOXveLL74o2rRpIwIDA0X58uVF/fr1xbhx44oFTGbe8n4LIUReXp6oV6+eaNeunc3n19rfdPPfK1s3My19tg1C2CiLTEREREQWuk8EJyIiIvIEBk1ERERECjBoIiIiIlKAQRMRERGRAgyaiIiIiBRg0ERERESkAIMmIiIiIgUYNBEREREpwKCJiIiISAEGTUREREQKMGgiIq+xePFiGAwGDBs2zOrjly5dQr169eDv74/k5GQPt46I9I5BExF5jQkTJiAyMhJr167FF198Uezx8ePHIy0tDfPmzUPTpk1VaCER6RkX7CUir5KSkoKWLVvC398ff/31F6pXrw4ASEhIQP/+/dG9e3ds2bIFBoNB5ZYSkd6wp4mIvEpoaCjefPNNnD17FuPGjQMAnDlzBuPGjUOVKlWwevVqBkxE5JByajeAiMjVRo8ejc8//xwJCQn4+OOPsWHDBpw/fx5xcXFo0KCB2s0jIp3i8BwReaVTp04hIiIC2dnZyM3NxQMPPICvvvpK7WYRkY5xeI6IvFK9evUwYcIE5Obmonz58li5cqXaTSIinWPQRERe6ezZs1ixYgUA4MaNG9i8ebPKLSIivWPQREReaezYsTh37hzmzZuH6tWrY8qUKTh58qTazSIiHWPQREReZ+3atdi0aRMeeOABzJgxA0uWLMGVK1cQHR2tdtOISMeYCE5EXsWcAO7j44M///wTderUAQD0798fCQkJWL58OcaMGaNyK4lIjxg0EZFX6dWrF77//nusX78egwYNsmw/d+4cwsPDkZOTg4MHD7L0ABHZjcNzROQ1VqxYge+//x79+vUrEjABQI0aNbBs2TJcuXIFo0aNAv+/SET2Yk8TEXmF48ePo1WrVsWWT7nV4MGD8fHHH2Pp0qV4+umnPdxKItIzBk1ERERECnB4joiIiEgBBk1ERERECjBoIiIiIlKAQRMRERGRAgyaiIiIiBRg0ERERESkAIMmIiIiIgUYNBEREREpwKCJiIiISAEGTUREREQKMGgiIiIiUoBBExEREZEC/w8HyWN1JFBrBwAAAABJRU5ErkJggg=="
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 6
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:25.183010Z",
     "start_time": "2025-03-14T10:12:24.345027Z"
    }
   },
   "cell_type": "code",
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "linear = LinearRegression()     # 此方法是最小二乘法直接求解，并未使用梯度下降\n",
    "linear.fit(X, y)"
   ],
   "id": "317feb70b9ad7f2b",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ],
      "text/html": [
       "<style>#sk-container-id-1 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: #000;\n",
       "  --sklearn-color-text-muted: #666;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-1 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-1 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-1 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: flex;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "  align-items: start;\n",
       "  justify-content: space-between;\n",
       "  gap: 0.5em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label .caption {\n",
       "  font-size: 0.6rem;\n",
       "  font-weight: lighter;\n",
       "  color: var(--sklearn-color-text-muted);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-1 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-1 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-1 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-1 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-1 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 0.5em;\n",
       "  text-align: center;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-1 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-1 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>LinearRegression</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 7
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:25.189236Z",
     "start_time": "2025-03-14T10:12:25.184015Z"
    }
   },
   "cell_type": "code",
   "source": "linear.coef_",
   "id": "f19b6dc38fb8bddd",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.77011339]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 8
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:25.204285Z",
     "start_time": "2025-03-14T10:12:25.189236Z"
    }
   },
   "cell_type": "code",
   "source": "linear.intercept_",
   "id": "a4b4ed7f2e354fad",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3.21509616])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 9
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## 梯度下降\n",
    "核心解决方案，不仅限于线性回归，其他算法中也有使用，如神经网络。"
   ],
   "id": "3f6a20970049a1f1"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 步长合适（小批量梯度下降算法）\n",
    "![](Linear/2.png)"
   ],
   "id": "777408f87d9659f8"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 步长太小（批量梯度算法）\n",
    "![](Linear/3.png)"
   ],
   "id": "3e6d9750f72500e2"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 步长太大（随机梯度算法）\n",
    "![](Linear/4.png)"
   ],
   "id": "a7406c49c73e2bdd"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 局部收敛（初始值选取或其他问题）\n",
    "![](Linear/5.png)"
   ],
   "id": "6d7750c61a11a23d"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 标准化（预处理）\n",
    "将不同量级的数据压缩至同一量级进行对比  \n",
    "\n",
    "![](Linear/6.png)"
   ],
   "id": "fed941af249e884b"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 批量梯度下降计算公式\n",
    "![](Linear/7.png)"
   ],
   "id": "dda740bda4495fad"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:25.971505Z",
     "start_time": "2025-03-14T10:12:25.929665Z"
    }
   },
   "cell_type": "code",
   "source": [
    "eta = 0.01\n",
    "n_iterations = 10000\n",
    "m = 100\n",
    "theta = np.zeros((2, 1))\n",
    "for iteration in range(n_iterations):\n",
    "    gradients = (1/m) * X01.T.dot(X01.dot(theta) - y)\n",
    "    theta -= eta * gradients\n",
    "theta"
   ],
   "id": "291c167d0e6e053b",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[3.21509618],\n",
       "       [4.77011337]])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 10
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:26.136264Z",
     "start_time": "2025-03-14T10:12:26.132360Z"
    }
   },
   "cell_type": "code",
   "source": "X_new.dot(theta)",
   "id": "efb0d6bfdadc9d25",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 3.21509618],\n",
       "       [12.75532291]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 11
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:26.316817Z",
     "start_time": "2025-03-14T10:12:26.311862Z"
    }
   },
   "cell_type": "code",
   "source": [
    "theta_path_bgd = []\n",
    "def plot_gradients_descent(eta, theta_path = False):\n",
    "    m = len(X01)\n",
    "    plt.plot(X, y, 'b.')\n",
    "    n_iterations = 1000\n",
    "    theta = np.zeros((2, 1))\n",
    "    for iterations in range(n_iterations):\n",
    "        if theta_path:\n",
    "            theta_path_bgd.append(theta.copy())\n",
    "        y_predict = X_new.dot(theta)\n",
    "        plt.plot(X_new[:, 1], y_predict, 'r-')\n",
    "        gradients = (1/m) * X01.T.dot(X01.dot(theta) - y)\n",
    "        theta -= eta * gradients\n",
    "    plt.axis((0, 2, 0, 15))\n",
    "    plt.title(f'eta = {eta}')"
   ],
   "id": "befc37b7931bfbe5",
   "outputs": [],
   "execution_count": 12
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:27.806294Z",
     "start_time": "2025-03-14T10:12:26.456126Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "plt.subplot(131)\n",
    "plot_gradients_descent(0.02)\n",
    "plt.subplot(132)\n",
    "plot_gradients_descent(0.1, True)\n",
    "plt.subplot(133)\n",
    "plot_gradients_descent(1)"
   ],
   "id": "e3ed245a0f4e5f79",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 1000x400 with 3 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 13
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:27.812683Z",
     "start_time": "2025-03-14T10:12:27.807304Z"
    }
   },
   "cell_type": "code",
   "source": "theta_path_bgd[:10]",
   "id": "908a75b21e57e984",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[0.],\n",
       "        [0.]]),\n",
       " array([[0.77007271],\n",
       "        [0.89132001]]),\n",
       " array([[1.37932184],\n",
       "        [1.60017055]]),\n",
       " array([[1.86098849],\n",
       "        [2.16420507]]),\n",
       " array([[2.24144884],\n",
       "        [2.61330194]]),\n",
       " array([[2.54163181],\n",
       "        [2.97117002]]),\n",
       " array([[2.77814395],\n",
       "        [3.25662266]]),\n",
       " array([[2.96416201],\n",
       "        [3.48458864]]),\n",
       " array([[3.11014122],\n",
       "        [3.66691435]]),\n",
       " array([[3.2243773 ],\n",
       "        [3.81300025]])]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 14
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 随机梯度下降\n",
    "![](Linear/8.png)"
   ],
   "id": "c439a2e287a01b1c"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:27.941978Z",
     "start_time": "2025-03-14T10:12:27.813265Z"
    }
   },
   "cell_type": "code",
   "source": [
    "theta_path_sgd = []\n",
    "m = len(X01)\n",
    "n_epochs = 50   # 迭代次数\n",
    "\n",
    "t0 = 5\n",
    "t1 = 50\n",
    "theta = np.zeros((2, 1))\n",
    "\n",
    "def learning_schedule(t):\n",
    "    \"\"\" 随着迭代次数的增加，学习率衰减\"\"\"\n",
    "    return t0 / (t1 + t)\n",
    "\n",
    "# 使用epoch的结构更容易理解和调整训练的次数：\n",
    "# 1. 通过外层循环 n_epochs ，可以明确模型看过整个数据集的次数。\n",
    "# 2. 在每个 epoch 结束后计算验证集误差，决定是否停止训练。若直接循环 5000 次，无法自然分割验证点。\n",
    "for epoch in range(n_epochs):\n",
    "    for _ in range(m):\n",
    "        if epoch <= 1 and _ < 10:\n",
    "            y_predict = X_new.dot(theta)\n",
    "            plt.plot(X_new[:, 1], y_predict, 'r-')\n",
    "        random_index = np.random.randint(m)\n",
    "        x_ = X01[random_index:random_index + 1]\n",
    "        y_ = y[random_index:random_index + 1]\n",
    "        gradients = x_.T.dot(x_.dot(theta) - y_)\n",
    "        eta = learning_schedule(epoch * m + _)\n",
    "        # 如果不加 .copy()，每次更新 theta 时都是在原地修改，列表中所有元素都指向最终的 theta 值\n",
    "        theta_path_sgd.append(theta.copy())\n",
    "        theta -= eta * gradients\n",
    "\n",
    "plt.plot(X, y, 'b.')\n",
    "plt.axis((0, 2, 0, 15))"
   ],
   "id": "2914b0a835130fcf",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.0), np.float64(2.0), np.float64(0.0), np.float64(15.0))"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 15
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:27.948552Z",
     "start_time": "2025-03-14T10:12:27.942983Z"
    }
   },
   "cell_type": "code",
   "source": "theta_path_sgd[:10]",
   "id": "c1aa63e36c9a4ebf",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[0.],\n",
       "        [0.]]),\n",
       " array([[0.76165622],\n",
       "        [0.65127855]]),\n",
       " array([[1.53185422],\n",
       "        [1.59377431]]),\n",
       " array([[1.74230017],\n",
       "        [1.61332491]]),\n",
       " array([[2.18770117],\n",
       "        [2.07897636]]),\n",
       " array([[2.46679408],\n",
       "        [2.36601474]]),\n",
       " array([[2.57422205],\n",
       "        [2.44266531]]),\n",
       " array([[2.84406864],\n",
       "        [2.72478065]]),\n",
       " array([[2.9103013 ],\n",
       "        [2.73465603]]),\n",
       " array([[3.00232034],\n",
       "        [2.80618745]])]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 16
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:27.958249Z",
     "start_time": "2025-03-14T10:12:27.948552Z"
    }
   },
   "cell_type": "code",
   "source": [
    "theta1 = [arr[0, 0] for arr in theta_path_sgd]\n",
    "theta2 = [arr[1, 0] for arr in theta_path_sgd]\n",
    "theta2[:10]"
   ],
   "id": "65fb143a12009a25",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[np.float64(0.0),\n",
       " np.float64(0.6512785483188889),\n",
       " np.float64(1.5937743093349024),\n",
       " np.float64(1.6133249111893395),\n",
       " np.float64(2.078976363670998),\n",
       " np.float64(2.3660147383762835),\n",
       " np.float64(2.442665305857711),\n",
       " np.float64(2.724780652228647),\n",
       " np.float64(2.7346560266269124),\n",
       " np.float64(2.8061874526622397)]"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 17
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:28.041884Z",
     "start_time": "2025-03-14T10:12:27.959660Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.plot(theta1, theta2, 'r-')\n",
    "plt.xlabel('theta1')\n",
    "plt.ylabel('theta2')"
   ],
   "id": "f5e6cd6b4428f667",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'theta2')"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 18
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### 小批量梯度下降(MiniBatch)",
   "id": "1dd6029c14b6dd66"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:28.251797Z",
     "start_time": "2025-03-14T10:12:28.042890Z"
    }
   },
   "cell_type": "code",
   "source": [
    "theta_path_mgd = []\n",
    "n_epochs = 50\n",
    "minibatch = 16\n",
    "theta = np.zeros((2, 1))\n",
    "\n",
    "t = -20\n",
    "for epoch in range(n_epochs):\n",
    "    shuffled_index = np.random.permutation(m)       # 洗牌操作\n",
    "    X01_shuffled = X01[shuffled_index]\n",
    "    y_shuffled = y[shuffled_index]\n",
    "    for _ in range(0, m, minibatch):\n",
    "        if epoch <= 50:\n",
    "            y_predict = X_new.dot(theta)\n",
    "            plt.plot(X_new[:, 1], y_predict, 'r-')\n",
    "        t += 1\n",
    "        x_ = X01_shuffled[_:_ + minibatch]\n",
    "        y_ = y_shuffled[_:_ + minibatch]\n",
    "        gradients = (1/minibatch) * x_.T.dot(x_.dot(theta) - y_)\n",
    "        eta = learning_schedule(t)\n",
    "        theta_path_mgd.append(theta.copy())\n",
    "        theta -= eta * gradients\n",
    "\n",
    "plt.plot(X, y, 'b.')\n",
    "plt.axis((0, 2, 0, 15))"
   ],
   "id": "619fad11119a42aa",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.0), np.float64(2.0), np.float64(0.0), np.float64(15.0))"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 19
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:28.258098Z",
     "start_time": "2025-03-14T10:12:28.252802Z"
    }
   },
   "cell_type": "code",
   "source": "theta_path_mgd[:10]",
   "id": "a267efbf2310f48d",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([[0.],\n",
       "        [0.]]),\n",
       " array([[1.42611663],\n",
       "        [2.03503677]]),\n",
       " array([[2.18132736],\n",
       "        [2.96672016]]),\n",
       " array([[2.61525264],\n",
       "        [3.43246339]]),\n",
       " array([[2.86598504],\n",
       "        [3.68592439]]),\n",
       " array([[3.0469297 ],\n",
       "        [3.88578746]]),\n",
       " array([[3.14160288],\n",
       "        [4.00575424]]),\n",
       " array([[3.15201106],\n",
       "        [4.02232663]]),\n",
       " array([[3.28277869],\n",
       "        [4.24009169]]),\n",
       " array([[3.36347323],\n",
       "        [4.3261973 ]])]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 20
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## 3种策略的对比实验",
   "id": "78298ca0fb83ac02"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:28.344924Z",
     "start_time": "2025-03-14T10:12:28.340283Z"
    }
   },
   "cell_type": "code",
   "source": [
    "theta_path_bgd = np.array(theta_path_bgd)\n",
    "theta_path_sgd = np.array(theta_path_sgd)\n",
    "theta_path_mgd = np.array(theta_path_mgd)"
   ],
   "id": "719792255cb5cfff",
   "outputs": [],
   "execution_count": 21
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:28.581419Z",
     "start_time": "2025-03-14T10:12:28.464024Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.figure(figsize=(8, 4))\n",
    "plt.plot(theta_path_bgd[:, 0], theta_path_bgd[:, 1], 'g-', linewidth=3, label='BGD')\n",
    "plt.plot(theta_path_sgd[:, 0], theta_path_sgd[:, 1], 'r-s', linewidth=1, label='SGD')\n",
    "plt.plot(theta_path_mgd[:, 0], theta_path_mgd[:, 1], 'b-o', linewidth=2, label='MINIGD')\n",
    "plt.axis((2.8, 3.8, 3.5, 5.3))\n",
    "plt.legend(loc='upper right')"
   ],
   "id": "adbe7e3538f220e3",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1b30bd07510>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 800x400 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 22
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "实际当中用MiniBatch较多，一般情况下选择batch数量应当越大越好。",
   "id": "182a0533e74d88c"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "## 多项式回归",
   "id": "8d7e98555ec7afa"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:28.796952Z",
     "start_time": "2025-03-14T10:12:28.792535Z"
    }
   },
   "cell_type": "code",
   "source": [
    "m = 100\n",
    "X = 4 * np.random.rand(m, 1)\n",
    "y = X ** 2 - 2 * X + np.random.randn(m, 1)"
   ],
   "id": "52337102531e990c",
   "outputs": [],
   "execution_count": 23
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:29.056586Z",
     "start_time": "2025-03-14T10:12:28.985737Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.plot(X, y, 'b.')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')"
   ],
   "id": "f7814f44086e5582",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 24
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:29.202665Z",
     "start_time": "2025-03-14T10:12:29.199052Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 多项式特征转换\n",
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n",
    "X_poly = poly_features.fit_transform(X)     # fit_transform() 学习规则 + 转换数据"
   ],
   "id": "96909b707474ca68",
   "outputs": [],
   "execution_count": 25
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:29.335263Z",
     "start_time": "2025-03-14T10:12:29.330863Z"
    }
   },
   "cell_type": "code",
   "source": "X[0]",
   "id": "eccfccd001b61c77",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.62471614])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 26
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:29.537832Z",
     "start_time": "2025-03-14T10:12:29.532375Z"
    }
   },
   "cell_type": "code",
   "source": "X_poly[0]",
   "id": "e63d1d4f79383c64",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2.62471614, 6.88913484])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 27
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:29.689104Z",
     "start_time": "2025-03-14T10:12:29.683997Z"
    }
   },
   "cell_type": "code",
   "source": "X[0] ** 2",
   "id": "b4915e94a8189f6",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([6.88913484])"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 28
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:29.868788Z",
     "start_time": "2025-03-14T10:12:29.862794Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 最小二乘法计算\n",
    "from sklearn.linear_model import LinearRegression\n",
    "linear = LinearRegression()\n",
    "linear.fit(X_poly, y)"
   ],
   "id": "dc930fb12c3d1b61",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ],
      "text/html": [
       "<style>#sk-container-id-2 {\n",
       "  /* Definition of color scheme common for light and dark mode */\n",
       "  --sklearn-color-text: #000;\n",
       "  --sklearn-color-text-muted: #666;\n",
       "  --sklearn-color-line: gray;\n",
       "  /* Definition of color scheme for unfitted estimators */\n",
       "  --sklearn-color-unfitted-level-0: #fff5e6;\n",
       "  --sklearn-color-unfitted-level-1: #f6e4d2;\n",
       "  --sklearn-color-unfitted-level-2: #ffe0b3;\n",
       "  --sklearn-color-unfitted-level-3: chocolate;\n",
       "  /* Definition of color scheme for fitted estimators */\n",
       "  --sklearn-color-fitted-level-0: #f0f8ff;\n",
       "  --sklearn-color-fitted-level-1: #d4ebff;\n",
       "  --sklearn-color-fitted-level-2: #b3dbfd;\n",
       "  --sklearn-color-fitted-level-3: cornflowerblue;\n",
       "\n",
       "  /* Specific color for light theme */\n",
       "  --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, white)));\n",
       "  --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, black)));\n",
       "  --sklearn-color-icon: #696969;\n",
       "\n",
       "  @media (prefers-color-scheme: dark) {\n",
       "    /* Redefinition of color scheme for dark theme */\n",
       "    --sklearn-color-text-on-default-background: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-background: var(--sg-background-color, var(--theme-background, var(--jp-layout-color0, #111)));\n",
       "    --sklearn-color-border-box: var(--sg-text-color, var(--theme-code-foreground, var(--jp-content-font-color1, white)));\n",
       "    --sklearn-color-icon: #878787;\n",
       "  }\n",
       "}\n",
       "\n",
       "#sk-container-id-2 {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 pre {\n",
       "  padding: 0;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-hidden--visually {\n",
       "  border: 0;\n",
       "  clip: rect(1px 1px 1px 1px);\n",
       "  clip: rect(1px, 1px, 1px, 1px);\n",
       "  height: 1px;\n",
       "  margin: -1px;\n",
       "  overflow: hidden;\n",
       "  padding: 0;\n",
       "  position: absolute;\n",
       "  width: 1px;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-dashed-wrapped {\n",
       "  border: 1px dashed var(--sklearn-color-line);\n",
       "  margin: 0 0.4em 0.5em 0.4em;\n",
       "  box-sizing: border-box;\n",
       "  padding-bottom: 0.4em;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-container {\n",
       "  /* jupyter's `normalize.less` sets `[hidden] { display: none; }`\n",
       "     but bootstrap.min.css set `[hidden] { display: none !important; }`\n",
       "     so we also need the `!important` here to be able to override the\n",
       "     default hidden behavior on the sphinx rendered scikit-learn.org.\n",
       "     See: https://github.com/scikit-learn/scikit-learn/issues/21755 */\n",
       "  display: inline-block !important;\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-text-repr-fallback {\n",
       "  display: none;\n",
       "}\n",
       "\n",
       "div.sk-parallel-item,\n",
       "div.sk-serial,\n",
       "div.sk-item {\n",
       "  /* draw centered vertical line to link estimators */\n",
       "  background-image: linear-gradient(var(--sklearn-color-text-on-default-background), var(--sklearn-color-text-on-default-background));\n",
       "  background-size: 2px 100%;\n",
       "  background-repeat: no-repeat;\n",
       "  background-position: center center;\n",
       "}\n",
       "\n",
       "/* Parallel-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item::after {\n",
       "  content: \"\";\n",
       "  width: 100%;\n",
       "  border-bottom: 2px solid var(--sklearn-color-text-on-default-background);\n",
       "  flex-grow: 1;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel {\n",
       "  display: flex;\n",
       "  align-items: stretch;\n",
       "  justify-content: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  position: relative;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:first-child::after {\n",
       "  align-self: flex-end;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:last-child::after {\n",
       "  align-self: flex-start;\n",
       "  width: 50%;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-parallel-item:only-child::after {\n",
       "  width: 0;\n",
       "}\n",
       "\n",
       "/* Serial-specific style estimator block */\n",
       "\n",
       "#sk-container-id-2 div.sk-serial {\n",
       "  display: flex;\n",
       "  flex-direction: column;\n",
       "  align-items: center;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  padding-right: 1em;\n",
       "  padding-left: 1em;\n",
       "}\n",
       "\n",
       "\n",
       "/* Toggleable style: style used for estimator/Pipeline/ColumnTransformer box that is\n",
       "clickable and can be expanded/collapsed.\n",
       "- Pipeline and ColumnTransformer use this feature and define the default style\n",
       "- Estimators will overwrite some part of the style using the `sk-estimator` class\n",
       "*/\n",
       "\n",
       "/* Pipeline and ColumnTransformer style (default) */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable {\n",
       "  /* Default theme specific background. It is overwritten whether we have a\n",
       "  specific estimator or a Pipeline/ColumnTransformer */\n",
       "  background-color: var(--sklearn-color-background);\n",
       "}\n",
       "\n",
       "/* Toggleable label */\n",
       "#sk-container-id-2 label.sk-toggleable__label {\n",
       "  cursor: pointer;\n",
       "  display: flex;\n",
       "  width: 100%;\n",
       "  margin-bottom: 0;\n",
       "  padding: 0.5em;\n",
       "  box-sizing: border-box;\n",
       "  text-align: center;\n",
       "  align-items: start;\n",
       "  justify-content: space-between;\n",
       "  gap: 0.5em;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label .caption {\n",
       "  font-size: 0.6rem;\n",
       "  font-weight: lighter;\n",
       "  color: var(--sklearn-color-text-muted);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:before {\n",
       "  /* Arrow on the left of the label */\n",
       "  content: \"▸\";\n",
       "  float: left;\n",
       "  margin-right: 0.25em;\n",
       "  color: var(--sklearn-color-icon);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {\n",
       "  color: var(--sklearn-color-text);\n",
       "}\n",
       "\n",
       "/* Toggleable content - dropdown */\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content {\n",
       "  max-height: 0;\n",
       "  max-width: 0;\n",
       "  overflow: hidden;\n",
       "  text-align: left;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content pre {\n",
       "  margin: 0.2em;\n",
       "  border-radius: 0.25em;\n",
       "  color: var(--sklearn-color-text);\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-toggleable__content.fitted pre {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {\n",
       "  /* Expand drop-down */\n",
       "  max-height: 200px;\n",
       "  max-width: 100%;\n",
       "  overflow: auto;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {\n",
       "  content: \"▾\";\n",
       "}\n",
       "\n",
       "/* Pipeline/ColumnTransformer-specific style */\n",
       "\n",
       "#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator-specific style */\n",
       "\n",
       "/* Colorize estimator box */\n",
       "#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted input.sk-toggleable__control:checked~label.sk-toggleable__label {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label label.sk-toggleable__label,\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  /* The background is the default theme color */\n",
       "  color: var(--sklearn-color-text-on-default-background);\n",
       "}\n",
       "\n",
       "/* On hover, darken the color of the background */\n",
       "#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "/* Label box, darken color on hover, fitted */\n",
       "#sk-container-id-2 div.sk-label.fitted:hover label.sk-toggleable__label.fitted {\n",
       "  color: var(--sklearn-color-text);\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Estimator label */\n",
       "\n",
       "#sk-container-id-2 div.sk-label label {\n",
       "  font-family: monospace;\n",
       "  font-weight: bold;\n",
       "  display: inline-block;\n",
       "  line-height: 1.2em;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-label-container {\n",
       "  text-align: center;\n",
       "}\n",
       "\n",
       "/* Estimator-specific */\n",
       "#sk-container-id-2 div.sk-estimator {\n",
       "  font-family: monospace;\n",
       "  border: 1px dotted var(--sklearn-color-border-box);\n",
       "  border-radius: 0.25em;\n",
       "  box-sizing: border-box;\n",
       "  margin-bottom: 0.5em;\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-0);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-0);\n",
       "}\n",
       "\n",
       "/* on hover */\n",
       "#sk-container-id-2 div.sk-estimator:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-2);\n",
       "}\n",
       "\n",
       "#sk-container-id-2 div.sk-estimator.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-2);\n",
       "}\n",
       "\n",
       "/* Specification for estimator info (e.g. \"i\" and \"?\") */\n",
       "\n",
       "/* Common style for \"i\" and \"?\" */\n",
       "\n",
       ".sk-estimator-doc-link,\n",
       "a:link.sk-estimator-doc-link,\n",
       "a:visited.sk-estimator-doc-link {\n",
       "  float: right;\n",
       "  font-size: smaller;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1em;\n",
       "  height: 1em;\n",
       "  width: 1em;\n",
       "  text-decoration: none !important;\n",
       "  margin-left: 0.5em;\n",
       "  text-align: center;\n",
       "  /* unfitted */\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted,\n",
       "a:link.sk-estimator-doc-link.fitted,\n",
       "a:visited.sk-estimator-doc-link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "div.sk-estimator:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link:hover,\n",
       ".sk-estimator-doc-link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "div.sk-estimator.fitted:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover,\n",
       "div.sk-label-container:hover .sk-estimator-doc-link.fitted:hover,\n",
       ".sk-estimator-doc-link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "/* Span, style for the box shown on hovering the info icon */\n",
       ".sk-estimator-doc-link span {\n",
       "  display: none;\n",
       "  z-index: 9999;\n",
       "  position: relative;\n",
       "  font-weight: normal;\n",
       "  right: .2ex;\n",
       "  padding: .5ex;\n",
       "  margin: .5ex;\n",
       "  width: min-content;\n",
       "  min-width: 20ex;\n",
       "  max-width: 50ex;\n",
       "  color: var(--sklearn-color-text);\n",
       "  box-shadow: 2pt 2pt 4pt #999;\n",
       "  /* unfitted */\n",
       "  background: var(--sklearn-color-unfitted-level-0);\n",
       "  border: .5pt solid var(--sklearn-color-unfitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link.fitted span {\n",
       "  /* fitted */\n",
       "  background: var(--sklearn-color-fitted-level-0);\n",
       "  border: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "\n",
       ".sk-estimator-doc-link:hover span {\n",
       "  display: block;\n",
       "}\n",
       "\n",
       "/* \"?\"-specific style due to the `<a>` HTML tag */\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link {\n",
       "  float: right;\n",
       "  font-size: 1rem;\n",
       "  line-height: 1em;\n",
       "  font-family: monospace;\n",
       "  background-color: var(--sklearn-color-background);\n",
       "  border-radius: 1rem;\n",
       "  height: 1rem;\n",
       "  width: 1rem;\n",
       "  text-decoration: none;\n",
       "  /* unfitted */\n",
       "  color: var(--sklearn-color-unfitted-level-1);\n",
       "  border: var(--sklearn-color-unfitted-level-1) 1pt solid;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted {\n",
       "  /* fitted */\n",
       "  border: var(--sklearn-color-fitted-level-1) 1pt solid;\n",
       "  color: var(--sklearn-color-fitted-level-1);\n",
       "}\n",
       "\n",
       "/* On hover */\n",
       "#sk-container-id-2 a.estimator_doc_link:hover {\n",
       "  /* unfitted */\n",
       "  background-color: var(--sklearn-color-unfitted-level-3);\n",
       "  color: var(--sklearn-color-background);\n",
       "  text-decoration: none;\n",
       "}\n",
       "\n",
       "#sk-container-id-2 a.estimator_doc_link.fitted:hover {\n",
       "  /* fitted */\n",
       "  background-color: var(--sklearn-color-fitted-level-3);\n",
       "}\n",
       "</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LinearRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator fitted sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label fitted sk-toggleable__label-arrow\"><div><div>LinearRegression</div></div><div><a class=\"sk-estimator-doc-link fitted\" rel=\"noreferrer\" target=\"_blank\" href=\"https://scikit-learn.org/1.6/modules/generated/sklearn.linear_model.LinearRegression.html\">?<span>Documentation for LinearRegression</span></a><span class=\"sk-estimator-doc-link fitted\">i<span>Fitted</span></span></div></label><div class=\"sk-toggleable__content fitted\"><pre>LinearRegression()</pre></div> </div></div></div></div>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 29
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:30.047398Z",
     "start_time": "2025-03-14T10:12:30.042864Z"
    }
   },
   "cell_type": "code",
   "source": "linear.coef_",
   "id": "eb3007b400de380c",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-2.06229782,  1.00640056]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 30
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:30.225684Z",
     "start_time": "2025-03-14T10:12:30.220901Z"
    }
   },
   "cell_type": "code",
   "source": "linear.intercept_",
   "id": "cdee9cbd9cf04a05",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.07348369])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 31
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:30.513834Z",
     "start_time": "2025-03-14T10:12:30.419775Z"
    }
   },
   "cell_type": "code",
   "source": [
    "X_new = np.linspace(0, 4, 100).reshape(100, 1)\n",
    "X_new_poly = poly_features.transform(X_new)     # transform() 直接应用规则，计算训练集\n",
    "y_new = linear.predict(X_new_poly)      # 用训练集预测值\n",
    "plt.plot(X, y, 'b.')\n",
    "plt.plot(X_new, y_new, 'r-')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')"
   ],
   "id": "5a5558fd34d21c1b",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'y')"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 32
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### 多项式维度对结果的影响",
   "id": "5147cad222a0cdb9"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:31.089904Z",
     "start_time": "2025-03-14T10:12:30.777066Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# Pipeline 可以将数据预处理步骤和模型训练步骤封装为一个整体对象，无需手动传递中间结果。\n",
    "from sklearn.pipeline import Pipeline\n",
    "# 未标准化的高阶特征（如x5）可能因数值范围过大，主导模型训练，导致低阶特征（如x）的系数被迫调整以补偿量纲差异，影响参数可解释性，因此需要 StandardScaler 标准化\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "plt.figure(figsize=(12, 6))\n",
    "for style, width, degree in (('r-', 3, 100), ('g--', 2, 2), ('y-+', 1, 1)):\n",
    "    poly_features = PolynomialFeatures(degree=degree, include_bias=False)\n",
    "    poly_standard = StandardScaler()\n",
    "    poly_linear = LinearRegression()\n",
    "    poly_pipeline = Pipeline([\n",
    "        ('PolynomialFeatures', poly_features), \n",
    "        ('StandardScaler', poly_standard), \n",
    "        ('LinearRegression', poly_linear)\n",
    "    ])\n",
    "    poly_pipeline.fit(X, y)     # 自动处理所有转换步骤的拟合和转换\n",
    "    y_new_predict = poly_pipeline.predict(X_new)        # 自动应用转换步骤\n",
    "    plt.plot(X_new, y_new_predict, style, linewidth=width, label='degree = ' + str(degree))\n",
    "\n",
    "plt.plot(X, y, 'b.')\n",
    "plt.axis((0, 4, -3, 9))\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('y')\n",
    "plt.legend(loc='upper center')"
   ],
   "id": "117514a6bd974283",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1b30bc86a50>"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 33
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "特征变换的越复杂，得到的结果过拟合风险越高，不建议做得特别复杂。",
   "id": "24eac3b095b4746"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### 数据样本数量对结果的影响",
   "id": "bd84c6c33fc5cb44"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:31.158310Z",
     "start_time": "2025-03-14T10:12:31.152054Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 评估均方误差(MSE)，是预测值与实际值之差的平方的平均值\n",
    "from sklearn.metrics import mean_squared_error\n",
    "from sklearn.model_selection import train_test_split        # 数据切分\n",
    "\n",
    "def plot_learning_curves(model, X, y):\n",
    "    X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=1)\n",
    "    train_errors, val_errors = [], []\n",
    "    for _ in range(1, len(X_train)):\n",
    "        model.fit(X_train[:_], y_train[:_])     # 不同数量的训练\n",
    "        y_train_predict = model.predict(X_train[:_])\n",
    "        y_val_predict = model.predict(X_val)\n",
    "        train_errors.append(mean_squared_error(y_train[:_], y_train_predict))\n",
    "        val_errors.append(mean_squared_error(y_val, y_val_predict))\n",
    "    plt.plot(np.sqrt(train_errors), 'r-+', label='train_errors')\n",
    "    plt.plot(np.sqrt(val_errors), 'b--', label='val_errors')    # np.sqrt() 是为了数据呈现更明显，即均方根误差\n",
    "    # MSE 开根号后相当于整体的预测值与实际值之间的差距，又被称为均方根误差(RMSE)\n",
    "    # RMSE 越趋近于 0 越好，它本质是平均误差。\n",
    "    plt.xlabel('Training set size')\n",
    "    plt.ylabel('RMSE')\n",
    "    plt.legend()"
   ],
   "id": "546c6bceec68e220",
   "outputs": [],
   "execution_count": 34
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:31.480664Z",
     "start_time": "2025-03-14T10:12:31.317713Z"
    }
   },
   "cell_type": "code",
   "source": [
    "linear = LinearRegression()\n",
    "plot_learning_curves(linear, X_poly, y)"
   ],
   "id": "944f8d9a4c766793",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 35
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "数据量越少，训练集的效果会越好，但实际测试效果很一般。  \n",
    "实际做模型的时候需要参考测试集和验证集的效果。"
   ],
   "id": "fe35ea5737fe2060"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "### 多项式回归的过拟合风险（degree不能过大）",
   "id": "b1ba502c3747c2bc"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:12:31.874267Z",
     "start_time": "2025-03-14T10:12:31.667571Z"
    }
   },
   "cell_type": "code",
   "source": [
    "pipeline = Pipeline([\n",
    "        ('PolynomialFeatures', PolynomialFeatures(degree=10, include_bias=False)), \n",
    "        ('LinearRegression', LinearRegression())\n",
    "])\n",
    "plot_learning_curves(pipeline, X, y)\n",
    "plt.axis((0, 80, 0, 5))"
   ],
   "id": "1c6f421149a5c80f",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(np.float64(0.0), np.float64(80.0), np.float64(0.0), np.float64(5.0))"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 36
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "越复杂越过拟合",
   "id": "bc4c2d887a07ccbb"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "## 正则化\n",
    "对权重参数进行惩罚，让权重参数尽可能平滑一些。"
   ],
   "id": "a1b3a079d01af6e5"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### 岭回归\n",
    "![](Linear/9.png)"
   ],
   "id": "467fabbb215c57b1"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:13:03.955863Z",
     "start_time": "2025-03-14T10:13:03.947783Z"
    }
   },
   "cell_type": "code",
   "source": [
    "from sklearn.linear_model import Ridge\n",
    "np.random.seed(42)\n",
    "m = 20\n",
    "X = 3 * np.random.rand(m, 1)\n",
    "y = 0.5 * X + np.random.randn(m, 1) / 1.5 + 1\n",
    "X_new = np.linspace(0, 3, 100).reshape(100, 1)"
   ],
   "id": "80752c5a611c5cca",
   "outputs": [],
   "execution_count": 41
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:13:09.410386Z",
     "start_time": "2025-03-14T10:13:09.403984Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def plot_ridge_returns(model_class, alpha, style):\n",
    "    model = model_class(alpha)\n",
    "    ridge = Pipeline([\n",
    "        ('PolynomialFeatures', PolynomialFeatures(degree=10, include_bias=False)), \n",
    "        ('StandardScaler', StandardScaler()), \n",
    "        ('RidgeRegression', model)\n",
    "    ])\n",
    "    ridge.fit(X, y)\n",
    "    y_new_regular = ridge.predict(X_new)\n",
    "    plt.plot(X_new, y_new_regular, style, label=f'alpha = {alpha}')"
   ],
   "id": "f3acf179c0709f93",
   "outputs": [],
   "execution_count": 44
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:13:09.936621Z",
     "start_time": "2025-03-14T10:13:09.836102Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# 学习率越大，正则化权重越大，回归越平稳\n",
    "plot_ridge_returns(Ridge, alpha=0, style='r:')\n",
    "plot_ridge_returns(Ridge, alpha=10**-5, style='g--')\n",
    "plot_ridge_returns(Ridge, alpha=1, style='b-')\n",
    "plt.plot(X, y, 'b.')\n",
    "plt.legend()"
   ],
   "id": "800cea428debdac9",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1b30f475250>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 45
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "惩罚力度越大，alpha值越大的时候，得到的决策方程越平稳。",
   "id": "606baefc76dcc20b"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": [
    "### Lasso 回归\n",
    "![](Linear/10.png)"
   ],
   "id": "9bd42a5b51cfa78d"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-03-14T10:13:29.927967Z",
     "start_time": "2025-03-14T10:13:29.790734Z"
    }
   },
   "cell_type": "code",
   "source": [
    "from sklearn.linear_model import Lasso\n",
    "plot_ridge_returns(Lasso, alpha=0.01, style='r:')\n",
    "plot_ridge_returns(Lasso, alpha=0.1, style='g--')\n",
    "plot_ridge_returns(Lasso, alpha=1, style='b-')\n",
    "plt.plot(X, y, 'b.')\n",
    "plt.legend()"
   ],
   "id": "f95d0bcbd076033d",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x1b30c2325d0>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "execution_count": 49
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "多做实验，得出结果！！！",
   "id": "ade1d4502de97586"
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
